Modeling Wearables Endpoints

Endpoints for Wearables Analysis

As described in the statistical analysis plan (SAP), the day- and nighttime endpoints we will consider for the wearables analysis are:

  1. High physical activity
  2. Low physical activity (for day only)
  3. Relative physical activity
  4. Mean peak physical activity
  5. Heart rate (mean, 5th percentile, 95th percentile)

Other endpoints which we will analyze descriptively include step count and oxygen saturation.

Temporal patterns of biometrics

The first three days were considered represented a “baseline” or “week 0” for comparison though it should be noted that study drug administration was begun on day 0. Three days was chosen to maximize data from an initial time period while minimizing effects of intervention to mimic as closely as possible to a true pre-drug baseline which was not available for this substudy. Days 4-15 were considered as week 1, encompassing the remainder of the treatment period. After 15 days, we split the follow-up period into 7-day intervals during the follow-up period continuing through week 14.

Week 0
Week 1
Weeks 2-5
Weeks 6-10
Weeks 11-14
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
% of time in high activity 22.2 (9.6) 20.2 (17.2) 0.74 -1.7 (10.4) 1.7 (9.9) 0.27 0.2 (7.5) 1 (13.3) 0.63 -1.5 (8.7) 3.1 (11.6) 0.16 -2.2 (3.6) 2 (8.4) 0.12
HR median 61.5 (12.5) 61.8 (11.7) 0.46 -1.4 (6.1) 1.8 (4.2) 0.25 -0.3 (4.1) 1 (6.6) 0.31 0.8 (6.9) 0.5 (6.9) 0.64 0 (8.3) 1.4 (7.5) 0.27
HR SD 4.2 (2.2) 3.8 (2.2) 0.08 -0.4 (2.5) 0.1 (2.3) 0.14 0.3 (3.7) 0.1 (2.5) 0.49 0.2 (3.1) 0.5 (2.6) 0.16 0.6 (3.2) 0.3 (2.4) 0.38
HR 5th percentile 56.6 (11.3) 56 (10.3) 0.40 0.4 (4.9) 1.2 (3.7) 0.34 -0.5 (2.2) 1.5 (4.6) 0.44 0 (2.7) -0.4 (5.8) 0.86 -0.4 (4.7) 1.1 (5.3) 0.24
HR 95th percentile 76.4 (13.6) 69.8 (17.4) 0.32 -4.5 (12) 2.7 (8.4) 0.10 -2.9 (9.7) 1.8 (14.9) 0.19 -1.7 (10.1) 1.4 (11.9) 0.22 -3 (12) 1.8 (14) 0.13
HRV median 44 (27) 35 (23.5) 0.73 4.3 (18.4) 1 (11.5) 0.72 5.6 (19.3) -0.2 (15.1) 0.36 5.5 (20.6) 1.5 (18.8) 0.37 4.7 (24.8) 1.9 (15.5) 0.21
RHR median 70.5 (8.8) 61.8 (10.2) 0.07 -3.1 (7.4) 1.8 (5.8) 0.37 -4.3 (6.4) 1.7 (8.8) 0.08 -3.2 (4.1) 0.7 (4.8) 0.42 -2.9 (5.9) 1.5 (6.3) 0.45
WHR median 89 (12.8) 76.8 (13) 0.27 -7.1 (35.6) 13.9 (21.8) 0.46 -8.2 (10.3) 7.4 (15.6) 0.30 -15.8 (32.8) -0.3 (28.6) 0.75 -15.2 (37.6) -4.8 (20.2) 1.00
O2 median 96.2 (0.8) 96.1 (2) 0.79 0 (0.8) 0 (2.1) 0.86 0.1 (1.1) 0 (1.7) 0.64 0 (1.2) -0.2 (1.3) 0.80 0.2 (1.2) -0.3 (2.2) 0.69
O2 5th percentile 94.3 (1.8) 94 (3.5) 0.63 0.1 (1.2) 0 (2.7) 0.81 0.5 (0.7) -0.1 (3.1) 0.91 0.1 (0.9) -0.3 (2.6) 0.82 0.3 (1) -0.3 (2.6) 0.47
SC median 0 (0) 0 (0) 0.02 0 (0) 0 (0) 0.85 0 (0) 0 (0) 0.45 0 (0) 0 (46.1) 0.22 0 (3) 0 (0) 0.68
Peak activity 318 (644.8) 357 (552.5) 0.93 -24.2 (324.2) 82.1 (285.7) 0.06 -16.8 (514) 49.4 (328) 1.00 30.5 (436.7) 101.3 (314.7) 0.39 -32.1 (505.2) 19.7 (324.9) 0.41
Week 0
Week 1
Weeks 2-5
Weeks 6-10
Weeks 11-14
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
% of time in high activity 23.6 (14.7) 23.9 (11.8) 0.77 1.2 (4.6) -1.3 (13.2) 1.00 -0.2 (8.2) 1.1 (8.5) 0.93 0.2 (7.7) 2.1 (9.1) 0.81 2 (6.4) 2.6 (11.8) 0.94
% of time in low activity 28.1 (7) 25.3 (16.2) 0.76 -1.2 (3.9) 0.4 (11.8) 0.56 -3.1 (7.7) -1.1 (11.6) 0.57 -3.4 (5.8) -0.2 (9.2) 0.28 -3.6 (6.7) -2.1 (13.7) 0.71
Relative activity -8.1 (46.6) -1 (55.7) 0.77 5.9 (13.9) -6.1 (42) 0.30 12.3 (26.9) 4.3 (34.8) 0.58 9.9 (20.2) 1.1 (35.2) 0.49 15.2 (39.2) 5.7 (41.6) 0.61
HR median 75 (11.2) 72.9 (17.2) 0.25 -1.1 (4.6) 1.7 (7) 0.05 -0.6 (8.6) 1.4 (7.1) 0.15 -0.8 (4.8) 0.1 (6.7) 0.77 -0.6 (5.6) 0.8 (8.6) 0.69
HR SD 14.2 (5.8) 10.7 (4) 0.02 -1.1 (4) 0.5 (2.5) 0.16 -1 (2.3) 0.8 (2.9) 0.03 -0.2 (2.2) 0.6 (3.2) 0.38 0.2 (3.6) 0.8 (3) 0.78
HR 5th percentile 62 (12.2) 59.1 (12.7) 0.43 -2 (2.4) 1.1 (4.4) 0.01 -2.3 (2.4) 1 (5.3) 0.03 -1.6 (5.4) -0.2 (3.9) 0.28 -3 (3.1) 0.8 (5.7) 0.05
HR 95th percentile 101.6 (19.2) 91 (15) 0.01 -4.4 (2) 4 (9.9) 0.00 -5.2 (6.2) 3.6 (10.9) 0.01 -3.1 (4.9) 2.8 (11.3) 0.10 -0.6 (12) 2.7 (11.8) 0.24
HRV median 28.2 (24.9) 33 (19.5) 0.98 1.7 (4.5) -0.5 (9.4) 0.23 5 (6.7) -0.5 (8.8) 0.17 5.3 (6.4) 0.8 (8.7) 0.15 4 (4.7) -0.4 (11.9) 0.14
RHR median 62.8 (11.6) 59 (13.1) 0.18 -2.2 (4.6) 2.3 (6.3) 0.04 -1.4 (2.5) 1.7 (5.9) 0.02 -2.1 (3.8) 1.5 (5.6) 0.05 -1.8 (3.8) 2.3 (6.9) 0.01
WHR median 100.5 (22.4) 94.1 (22.8) 0.52 -2.8 (11.7) 0.1 (9.9) 0.48 -1.8 (13.7) -0.5 (14.3) 0.47 -2.8 (11.5) -1.6 (13.5) 0.75 0.1 (10.5) -3.7 (12) 0.63
O2 median 96.3 (2) 97 (2.6) 0.61 0.1 (1.1) 0.1 (1.4) 0.92 0.1 (1.7) -0.4 (1.3) 0.20 -0.1 (1.5) -0.3 (1.9) 0.37 0.5 (1.2) -0.4 (1.3) 0.03
O2 5th percentile 94.3 (2.3) 93.5 (2.3) 0.35 -0.4 (2.6) 0.3 (2) 0.41 0 (2.1) 0.2 (2.1) 0.68 -0.1 (1.8) 0.2 (2.3) 0.65 0.2 (2) 0.3 (2.6) 0.85
SC median 1248 (2616) 480 (1680) 0.40 128 (1692) 14 (1123.6) 0.56 273.9 (1073.7) 583.2 (888.4) 0.09 85.7 (1005.3) 160 (1235.2) 0.48 -136.3 (1656.5) 260.2 (1433.6) 0.32
Peak activity 1625 (104.5) 1669.5 (117) 0.26 -17.9 (108.6) -6.4 (91.2) 0.94 38.9 (90.8) 16.4 (99.4) 0.55 6.3 (98.1) -2.7 (126.4) 0.52 31 (113.4) -5.5 (176.6) 0.32
Week 0
Week 1
Weeks 2-5
Weeks 6-10
Weeks 11-14
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
% of time in high activity 19.4 (11) 19 (18.3) 0.60 -0.2 (5.6) 0.4 (9.7) 0.85 1.5 (15) -0.1 (13.7) 0.24 1.1 (8.5) 3.1 (9.3) 0.99 0.3 (7.4) 0.6 (9) 0.96
HR median 61.5 (12.6) 62 (11.4) 0.79 -2.7 (5.9) 1.9 (4.3) 0.06 -0.8 (2.4) 0.5 (6.5) 0.21 -1.7 (9.6) 0.5 (5.1) 0.19 -2.7 (11.1) 1.6 (7.7) 0.08
HR SD 5.3 (2.1) 3.7 (1.9) 0.05 -2.2 (2.7) 0.2 (2.1) 0.05 -0.9 (3.4) 0.3 (2.4) 0.21 -1.9 (2.9) 0.2 (2.1) 0.03 -1.4 (3.3) 0.2 (2.5) 0.06
HR 5th percentile 56.6 (11.3) 56 (10.1) 0.68 -1.3 (4.5) 1.2 (3.8) 0.19 -0.5 (1.1) 1.2 (5.8) 0.49 -0.8 (4.4) -0.4 (4.2) 0.35 -1.4 (7.2) 1.1 (6.6) 0.12
HR 95th percentile 76.4 (12.6) 69.8 (17.5) 0.50 -5.3 (7.5) 2.7 (8.1) 0.02 -5.1 (7.1) 1.7 (11.6) 0.09 -6.2 (9) 1.5 (11.1) 0.03 -7.5 (10.4) 2.8 (13.2) 0.03
HRV median 44 (23.2) 42.8 (27.9) 1.00 0.7 (20.1) 1.6 (18.5) 0.61 2 (17.8) 2 (20.7) 0.82 3.7 (23.8) 3.4 (21) 0.51 4.7 (24.3) 1.6 (16.7) 0.31
RHR median 69.5 (14.5) 62.5 (11) 0.18 -0.5 (7.1) 1.8 (4.6) 0.64 -0.7 (6) 1.2 (7.2) 0.45 -4.7 (3.9) 0.1 (4) 0.26 -0.9 (5.6) 1.7 (5) 0.52
WHR median 90 (17.5) 79.9 (16.9) 0.77 -14.1 (16.1) -6.5 (10.8) 0.66 -9.5 (6.9) -3.7 (3.6) 0.77 -21 (0) 1.4 (16.5) 0.33 -15.2 (0) 1.5 (12.3) 0.38
O2 median 96.2 (0.7) 96.2 (2.2) 1.00 0 (0.6) 0.4 (2.7) 0.56 0.4 (0.8) 0.2 (2.6) 0.99 0.1 (1) 0 (2.1) 0.99 0.2 (1) 0 (2.6) 0.93
O2 5th percentile 94.3 (1.7) 94 (3.6) 0.48 0.1 (1.2) 0.1 (3.9) 0.55 0.5 (1.4) 1 (3.1) 0.48 0.1 (0.9) 0.2 (3.2) 0.41 0.3 (0.9) 0.5 (3.2) 0.56
SC median 0 (0) 0 (0) 0.02 0 (0) 0 (0) 0.86 0 (0) 0 (0) 0.59 0 (0) 0 (47) 0.23 0 (0) 0 (0) 0.26
Peak activity 424.5 (662.4) 324.5 (541.8) 0.72 -37.2 (371) 78.3 (189.8) 0.08 -21.1 (764.4) 39.3 (290.2) 0.80 8.5 (494.1) 47.8 (247.5) 0.50 -58 (553) 13.5 (322) 0.40
Week 0
Week 1
Weeks 2-5
Weeks 6-10
Weeks 11-14
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
Placebo
Treatment
P
% of time in high activity 23.5 (12.6) 24.8 (11.7) 0.64 1.2 (4.6) -2 (12.8) 0.60 0.2 (7.3) 1.1 (8) 0.90 0.3 (6.9) -0.8 (7.7) 0.38 2.1 (5) 2.9 (12.1) 0.75
% of time in low activity 28.2 (4.2) 25.3 (11.9) 0.33 0 (4.1) 0.4 (8.8) 0.64 -3.4 (6.8) -0.4 (8.6) 0.44 -3.6 (2) -0.2 (7.6) 0.10 -3.6 (3.7) -1.1 (10.5) 0.27
Relative activity -8.1 (31.8) 3.7 (46.5) 0.44 6.3 (13.1) -7.7 (35.2) 0.21 13 (22) 2.4 (32) 0.46 11.2 (16.1) 0.2 (31.8) 0.16 16 (19.5) 4.7 (37.9) 0.19
HR median 73.5 (11.3) 72.8 (13.8) 0.43 -0.6 (3.8) 1.7 (7) 0.07 -0.6 (7.1) 1.3 (6.3) 0.19 -0.8 (3.7) 0.1 (6.3) 0.96 0 (6.7) -0.8 (7.4) 0.93
HR SD 15.5 (4.2) 10.7 (4) 0.01 -1.6 (3.6) 0.6 (2.3) 0.09 -1.2 (2) 0.6 (3) 0.02 -0.5 (2.9) 0.7 (3.2) 0.39 -0.2 (3.1) 0.8 (3.5) 0.33
HR 5th percentile 59 (13) 59 (12.3) 0.68 -1.7 (3) 1.1 (4.5) 0.02 -2.3 (1.8) -0.3 (5.8) 0.11 -1.6 (6.1) 0 (5.1) 0.37 -3 (3.2) 0.2 (5.8) 0.13
HR 95th percentile 108.1 (21.5) 90.2 (15.5) 0.01 -4.4 (1.4) 4.4 (8.8) 0.00 -6.7 (7.5) 3.8 (9.5) 0.00 -3.2 (5.6) 2.9 (10.6) 0.08 -4.8 (12.3) 3.2 (7.5) 0.10
HRV median 25.4 (31) 38.6 (14.8) 0.57 1.7 (3.7) -2.9 (10.4) 0.12 5 (6) -1.3 (9.8) 0.13 5.3 (6.9) -0.7 (11.3) 0.21 4.7 (5) -3.1 (12.3) 0.24
RHR median 61.5 (14) 58.1 (13.4) 0.39 -2.1 (5.1) 2.1 (5.6) 0.16 -1.3 (3.2) 0.6 (7.9) 0.16 -2.1 (5.3) 1.5 (6.9) 0.09 -1.8 (4.3) 2.1 (5.8) 0.02
WHR median 100.6 (26.6) 100.6 (22.5) 0.58 -0.1 (15.9) 0 (9.9) 0.61 -3.1 (16.2) -2.2 (12.2) 0.45 -6.4 (13.3) -2 (11) 0.43 -0.2 (14.5) -3.6 (10.3) 0.85
O2 median 97 (1.8) 97.2 (2.2) 0.79 -0.1 (0.9) 0.3 (1.5) 0.39 -0.2 (1.4) -0.1 (1.5) 0.81 -0.1 (1.3) -0.3 (1.9) 0.55 0.1 (1.2) -0.4 (1.5) 0.14
O2 5th percentile 94.8 (1.9) 93.8 (2.2) 0.17 -0.5 (2.2) 0.8 (2.6) 0.10 -0.3 (1.7) 0.6 (1.8) 0.09 -0.3 (2) 0.4 (2.3) 0.13 0.1 (2.2) 0.3 (2.4) 0.47
SC median 924 (2494) 624 (1668) 0.84 276 (1457.6) 92 (1304) 0.68 288.7 (992) 583.2 (1037.3) 0.21 178.5 (939.9) 189 (1159.3) 0.82 556.8 (1220.5) 243.6 (1688) 0.82
Peak activity 1629 (88.2) 1669.5 (134.2) 0.36 15.6 (112.6) 2.3 (88.3) 0.55 27.4 (81.2) 3.6 (113.5) 0.64 -0.4 (87.9) -1.9 (114.1) 0.53 24.6 (111.4) -0.2 (153.9) 0.27

Mixed models for repeated measures (MMRM)

Latent Class Trajectory Modeling (LCMM)

In order to perform model selection for each endpoint, we will identify the models with the lowest BIC values and visualize the resulting clusters to assess cluster consistency. The model adequacy metric interpretations as given by the LCTMtoolkit package are as follows:

  • Model-specific:
    • Entropy: close to zero
    • Relative entropy: close to 1
  • Class-specific:
    • APPA: greater than 0.7
    • OCC: greater than 5
    • Mismatch: close to 0
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 30198.77 30217.89 5.5115538 0.8409702 24 (48%) 26 (52%) NA NA NA
2 30178.49 30205.26 5.2477097 0.9044666 9 (18%) 18 (36%) 23 (46%) NA NA
2 30148.38 30182.79 1.9399013 0.9720131 9 (18%) 16 (32%) 21 (42%) 4 (8%) NA
2 30141.36 30183.42 6.7774679 0.9157784 8 (16%) 12 (24%) 12 (24%) 4 (8%) 14 (28%)
4 30209.69 30236.46 12.9254803 0.6270495 37 (74%) 13 (26%) NA NA NA
4 30211.92 30250.16 13.7808365 0.7491228 23 (46%) 7 (14%) 20 (40%) NA NA
4 30166.56 30216.27 4.9628847 0.9284007 16 (32%) 9 (18%) 11 (22%) 14 (28%) NA
4 30156.34 30217.52 5.7316433 0.9287746 11 (22%) 5 (10%) 11 (22%) 9 (18%) 14 (28%)
6 30203.21 30237.63 12.8741048 0.6285319 32 (64%) 18 (36%) NA NA NA
6 30197.81 30247.52 13.5607642 0.7531292 6 (12%) 30 (60%) 14 (28%) NA NA
6 30172.19 30237.20 4.5270620 0.9346883 9 (18%) 16 (32%) 11 (22%) 14 (28%) NA
6 30154.86 30235.16 3.2213969 0.9599687 5 (10%) 13 (26%) 7 (14%) 21 (42%) 4 (8%)
8 30179.66 30221.73 0.4585197 0.9867699 46 (92%) 4 (8%) NA NA NA
8 30180.75 30241.94 9.7444373 0.8226046 7 (14%) 33 (66%) 10 (20%) NA NA
8 30165.60 30245.91 10.3990663 0.8499732 18 (36%) 17 (34%) 13 (26%) 2 (4%) NA
8 30167.79 30267.22 3.4766945 0.9567962 5 (10%) 13 (26%) 7 (14%) 11 (22%) 14 (28%)

Mean predicted trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 9 18 23
participant_age (mean (SD)) 41.3 (10.3) 41 (14.7) 44.6 (13.2) 0.19
duration_symptoms_months (mean (SD)) 16.3 (11.6) 15.7 (10.1) 17 (9.1) 0.09
bmi (mean (SD)) 24.8 (4.1) 31.6 (8) 26.6 (4.8) 0.74
participant_sex = Male (%) 3 (33.3) 11 (61.1) 7 (30.4) 0.43
race (%) 0.8
Asian 0 (0) 1 (5.6) 3 (13)
Black or African American 1 (11.1) 0 (0) 1 (4.3)
White 6 (66.7) 17 (94.4) 17 (73.9)
More than one race 1 (11.1) 0 (0) 1 (4.3)
Other 1 (11.1) 0 (0) 1 (4.3)
ethnic = 1 (%) 1 (11.1) 1 (5.6) 4 (17.4) 0.25
bmi_group (%) 0.58
Underweight 0 (0) 1 (5.6) 1 (4.3)
Normal 5 (55.6) 4 (22.2) 9 (39.1)
Overweight 2 (22.2) 4 (22.2) 6 (26.1)
Obese 2 (22.2) 9 (50) 7 (30.4)
fatigue = 1 (%) 9 (100) 17 (94.4) 21 (91.3) 0.3
sob = 1 (%) 9 (100) 10 (55.6) 7 (30.4) 1.31
brainfog = 1 (%) 7 (77.8) 14 (77.8) 20 (87) 0.16
bodyaches = 1 (%) 7 (77.8) 7 (38.9) 14 (60.9) 0.56
heart = 1 (%) 8 (88.9) 8 (44.4) 12 (52.2) 0.7
stomach = 1 (%) 3 (33.3) 7 (38.9) 11 (47.8) 0.2
rand_assignment = Treatment (%) 7 (77.8) 13 (72.2) 17 (73.9) 0.09
high_phys (mean (SD)) 13.1 (3.2) 22.2 (2.7) 32.1 (3.6) 3.89
low_phys (mean (SD)) 32.1 (7) 25.6 (7.2) 19.6 (4.1) 1.38
rel_phys (mean (SD)) -0.4 (0.1) 0 (0.1) 0.2 (0.1) 3.13
mean_peak_phys (mean (SD)) 1477.8 (123.1) 1623.3 (50) 1697 (38.6) 1.87
heartRate_median_dt (mean (SD)) 72 (6) 71.9 (7.4) 76 (10.6) 0.31
heart_rate_pct5 (mean (SD)) 60.4 (6) 58 (6.3) 61.8 (8.8) 0.36
heart_rate_pct95 (mean (SD)) 93.8 (7.1) 98.2 (10.7) 102.1 (13.4) 0.53
heartRate_std_dt (mean (SD)) 10.8 (1.9) 13.1 (3.5) 13 (3.9) 0.52
heartRateVariability_median_dt (mean (SD)) 34 (11.1) 41.6 (19.4) 36.8 (18.1) 0.31
restingHeartRate_median_dt (mean (SD)) 60.6 (5.7) 59.5 (5.7) 62.9 (9.4) 0.31
walkingHeartRateAverage_median_dt (mean (SD)) 95.3 (12.5) 96.6 (11.6) 96.6 (12.8) 0.07
bloodOxygenSaturation_median_dt (mean (SD)) 96.7 (1.1) 96.4 (1.3) 96.2 (1) 0.33
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 93.3 (1.6) 93.2 (1.9) 93.9 (1.2) 0.31
stepCount_median_dt (mean (SD)) 218.9 (214.8) 1028.2 (672.4) 2583.2 (1170.8) 2.02
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 32532.33 32551.45 2.669122 0.9229854 35 (70%) 15 (30%) NA NA NA
2 32498.30 32525.07 2.148778 0.9608820 35 (70%) 12 (24%) 3 (6%) NA NA
2 32499.34 32533.75 11.264780 0.8374836 28 (56%) 7 (14%) 12 (24%) 3 (6%) NA
2 32480.35 32522.42 11.201844 0.8607981 25 (50%) 10 (20%) 10 (20%) 2 (4%) 3 (6%)
4 32539.93 32566.70 2.615965 0.9245192 35 (70%) 15 (30%) NA NA NA
4 32509.50 32547.74 2.169292 0.9605085 35 (70%) 12 (24%) 3 (6%) NA NA
4 32514.64 32564.35 12.417228 0.8208573 25 (50%) 10 (20%) 12 (24%) 3 (6%) NA
4 32526.64 32587.83 12.506111 0.8445903 0 (0%) 25 (50%) 10 (20%) 12 (24%) 3 (6%)
6 32543.83 32578.25 2.793250 0.9194038 35 (70%) 15 (30%) NA NA NA
6 32509.64 32559.36 2.562960 0.9533419 35 (70%) 12 (24%) 3 (6%) NA NA
6 32509.14 32574.15 5.757115 0.9169424 31 (62%) 5 (10%) 11 (22%) 3 (6%) NA
6 32480.83 32561.13 8.632538 0.8927261 23 (46%) 12 (24%) 9 (18%) 3 (6%) 3 (6%)
8 32538.50 32580.56 2.767159 0.9201567 36 (72%) 14 (28%) NA NA NA
8 32517.72 32578.91 3.854612 0.9298276 34 (68%) 10 (20%) 6 (12%) NA NA
8 32468.89 32549.19 1.931352 0.9721365 33 (66%) 2 (4%) 12 (24%) 3 (6%) NA
8 32419.53 32518.96 1.108177 0.9862290 33 (66%) 2 (4%) 1 (2%) 11 (22%) 3 (6%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 35 12 3
participant_age (mean (SD)) 43.3 (11.9) 41.4 (17.2) 41 (12.8) 0.11
duration_symptoms_months (mean (SD)) 13.5 (8) 22.9 (9.7) 23.9 (15) 0.67
bmi (mean (SD)) 28.1 (7) 28.8 (5) 24.5 (8.2) 0.4
participant_sex = Male (%) 14 (40) 6 (50) 1 (33.3) 0.23
race (%) 0.92
Asian 3 (8.6) 1 (8.3) 0 (0)
Black or African American 1 (2.9) 0 (0) 1 (33.3)
White 27 (77.1) 11 (91.7) 2 (66.7)
More than one race 2 (5.7) 0 (0) 0 (0)
Other 2 (5.7) 0 (0) 0 (0)
ethnic = 1 (%) 5 (14.3) 1 (8.3) 0 (0) 0.4
bmi_group (%) 0.96
Underweight 1 (2.9) 0 (0) 1 (33.3)
Normal 13 (37.1) 4 (33.3) 1 (33.3)
Overweight 8 (22.9) 4 (33.3) 0 (0)
Obese 13 (37.1) 4 (33.3) 1 (33.3)
fatigue = 1 (%) 33 (94.3) 11 (91.7) 3 (100) 0.29
sob = 1 (%) 19 (54.3) 6 (50) 1 (33.3) 0.29
brainfog = 1 (%) 30 (85.7) 9 (75) 2 (66.7) 0.3
bodyaches = 1 (%) 19 (54.3) 7 (58.3) 2 (66.7) 0.17
heart = 1 (%) 19 (54.3) 7 (58.3) 2 (66.7) 0.17
stomach = 1 (%) 11 (31.4) 8 (66.7) 2 (66.7) 0.5
rand_assignment = Treatment (%) 25 (71.4) 10 (83.3) 2 (66.7) 0.26
high_phys (mean (SD)) 19 (4.7) 35.2 (4) 54.5 (5.2) 5.02
low_phys (mean (SD)) 81 (4.7) 64.8 (4) 45.5 (5.2) 5.02
rel_phys (mean (SD)) -0.6 (0.1) -0.3 (0.1) 0.1 (0.1) 5.02
mean_peak_phys (mean (SD)) 401.3 (223.8) 752.2 (225.7) 1212.8 (167.8) 2.66
heartRate_median_n (mean (SD)) 63.5 (9) 66.3 (11.5) 67.2 (2) 0.32
heart_rate_pct5 (mean (SD)) 58.2 (8.2) 59.7 (9.2) 59.9 (1.2) 0.17
heart_rate_pct95 (mean (SD)) 71.2 (10.2) 77.4 (14.4) 81.2 (3.9) 0.72
heartRate_std_n (mean (SD)) 4.5 (1.4) 6.1 (2.2) 7.2 (1) 1.22
heartRateVariability_median_n (mean (SD)) 44.1 (22.4) 40.1 (11.5) 40.6 (12.1) 0.15
restingHeartRate_median_n (mean (SD)) 63.9 (9.8) 61.4 (10) 61.2 (1.9) 0.22
walkingHeartRateAverage_median_n (mean (SD)) 88.9 (11.9) 95.7 (19.6) 93.9 (13.1) 0.31
bloodOxygenSaturation_median_n (mean (SD)) 95.8 (1) 96.5 (0.8) 95.3 (0.4) 1.07
bloodOxygenSaturation_percentile_5_n (mean (SD)) 93.4 (1.4) 94.3 (0.7) 93.2 (0) 1.13
stepCount_median_n (mean (SD)) 0 (0.2) 0.3 (0.5) 0.8 (0.5) 1.23
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 30138.51 30157.63 5.4323182 0.8432564 43 (86%) 7 (14%) NA NA NA
2 30129.51 30156.27 9.8266226 0.8211085 19 (38%) 26 (52%) 5 (10%) NA NA
2 30107.70 30142.11 6.2118122 0.9103825 14 (28%) 21 (42%) 11 (22%) 4 (8%) NA
2 30107.96 30150.02 8.9079304 0.8893038 11 (22%) 5 (10%) 11 (22%) 19 (38%) 4 (8%)
4 30143.08 30169.85 6.2294969 0.8202547 41 (82%) 9 (18%) NA NA NA
4 30137.19 30175.43 8.0790195 0.8529232 17 (34%) 28 (56%) 5 (10%) NA NA
4 30115.91 30165.62 5.6617345 0.9183184 22 (44%) 13 (26%) 11 (22%) 4 (8%) NA
4 30119.97 30181.16 7.7111249 0.9041762 10 (20%) 5 (10%) 20 (40%) 11 (22%) 4 (8%)
6 30143.88 30178.30 6.0369004 0.8258119 36 (72%) 14 (28%) NA NA NA
6 30113.46 30163.18 6.3102490 0.8851233 36 (72%) 1 (2%) 13 (26%) NA NA
6 30113.69 30178.70 6.3230411 0.9087778 1 (2%) 36 (72%) 1 (2%) 12 (24%) NA
6 30127.01 30207.31 8.0643277 0.8997870 11 (22%) 6 (12%) 19 (38%) 9 (18%) 5 (10%)
8 30125.41 30167.47 0.0060325 0.9998259 48 (96%) 2 (4%) NA NA NA
8 30123.94 30185.13 6.2345331 0.8865017 36 (72%) 1 (2%) 13 (26%) NA NA
8 30122.16 30202.47 4.2911733 0.9380915 33 (66%) 4 (8%) 8 (16%) 5 (10%) NA
8 30116.40 30215.82 4.3224984 0.9462856 21 (42%) 13 (26%) 2 (4%) 9 (18%) 5 (10%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 19 26 5
participant_age (mean (SD)) 39 (10.7) 45.9 (14.8) 40.6 (9.8) 0.37
duration_symptoms_months (mean (SD)) 16.6 (9.2) 15.7 (10.1) 19.6 (11) 0.26
bmi (mean (SD)) 28 (6.3) 28.5 (7.1) 26.2 (5.5) 0.25
participant_sex = Male (%) 8 (42.1) 11 (42.3) 2 (40) 0.03
race (%) 0.64
Asian 2 (10.5) 2 (7.7) 0 (0)
Black or African American 1 (5.3) 1 (3.8) 0 (0)
White 15 (78.9) 20 (76.9) 5 (100)
More than one race 0 (0) 2 (7.7) 0 (0)
Other 1 (5.3) 1 (3.8) 0 (0)
ethnic = 1 (%) 3 (15.8) 3 (11.5) 0 (0) 0.42
bmi_group (%) 0.61
Underweight 1 (5.3) 0 (0) 1 (20)
Normal 6 (31.6) 11 (42.3) 1 (20)
Overweight 6 (31.6) 5 (19.2) 1 (20)
Obese 6 (31.6) 10 (38.5) 2 (40)
fatigue = 1 (%) 17 (89.5) 25 (96.2) 5 (100) 0.34
sob = 1 (%) 7 (36.8) 16 (61.5) 3 (60) 0.34
brainfog = 1 (%) 15 (78.9) 22 (84.6) 4 (80) 0.1
bodyaches = 1 (%) 9 (47.4) 16 (61.5) 3 (60) 0.19
heart = 1 (%) 14 (73.7) 11 (42.3) 3 (60) 0.44
stomach = 1 (%) 7 (36.8) 12 (46.2) 2 (40) 0.13
rand_assignment = Treatment (%) 14 (73.7) 19 (73.1) 4 (80) 0.11
high_phys (mean (SD)) 29.6 (6.2) 23.3 (7.6) 18 (7.8) 1.08
low_phys (mean (SD)) 17.1 (3.1) 26.1 (3.5) 39.3 (3.9) 4.16
rel_phys (mean (SD)) 0.2 (0.1) -0.1 (0.2) -0.4 (0.2) 2.31
mean_peak_phys (mean (SD)) 1675.1 (60) 1607 (118) 1588.6 (94.2) 0.66
heartRate_median_dt (mean (SD)) 78.6 (10) 70.7 (6.9) 71 (5.2) 0.64
heart_rate_pct5 (mean (SD)) 62.7 (8.7) 58.9 (6.9) 56.6 (2.6) 0.63
heart_rate_pct95 (mean (SD)) 106.2 (11.8) 93.7 (8.7) 99.7 (11.8) 0.78
heartRate_std_dt (mean (SD)) 13.9 (3.9) 11.3 (2.8) 14.1 (3.5) 0.57
heartRateVariability_median_dt (mean (SD)) 40.2 (19) 36.4 (17.9) 38.3 (9.2) 0.16
restingHeartRate_median_dt (mean (SD)) 64.9 (8.8) 59.4 (6.2) 56.4 (2.7) 0.88
walkingHeartRateAverage_median_dt (mean (SD)) 101.6 (12) 91.9 (10.9) 98.7 (11.9) 0.56
bloodOxygenSaturation_median_dt (mean (SD)) 96.5 (1.1) 96.1 (1.2) 96.9 (0.5) 0.6
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 94.1 (1.4) 93 (1.5) 93.6 (2) 0.49
stepCount_median_dt (mean (SD)) 2037.3 (1317.7) 1494.2 (1275.4) 466.5 (553.1) 1.01
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 1502.556 1521.676 4.8981310 0.8586698 23 (46%) 27 (54%) NA NA NA
2 1474.448 1501.217 1.1581710 0.9789157 5 (10%) 19 (38%) 26 (52%) NA NA
2 1453.461 1487.877 4.3522558 0.9372102 5 (10%) 17 (34%) 11 (22%) 17 (34%) NA
2 1447.409 1489.474 5.9058228 0.9266101 5 (10%) 12 (24%) 11 (22%) 7 (14%) 15 (30%)
4 1506.071 1532.839 4.6261762 0.8665168 23 (46%) 27 (54%) NA NA NA
4 1480.135 1518.375 0.8383435 0.9847381 5 (10%) 19 (38%) 26 (52%) NA NA
4 1462.444 1512.157 4.3003787 0.9379587 5 (10%) 17 (34%) 17 (34%) 11 (22%) NA
4 1456.341 1517.526 4.7395711 0.9411028 5 (10%) 12 (24%) 7 (14%) 15 (30%) 11 (22%)
6 1499.957 1534.373 3.4432046 0.9006501 8 (16%) 42 (84%) NA NA NA
6 1490.130 1539.842 5.7764880 0.8948403 9 (18%) 15 (30%) 26 (52%) NA NA
6 1504.622 1569.631 17.1138088 0.7530999 9 (18%) 17 (34%) 15 (30%) 9 (18%) NA
6 1498.973 1579.278 15.1702000 0.8114845 9 (18%) 14 (28%) 1 (2%) 16 (32%) 10 (20%)
8 1492.348 1534.413 7.9696514 0.7700445 13 (26%) 37 (74%) NA NA NA
8 1483.852 1545.037 8.0743368 0.8530084 8 (16%) 12 (24%) 30 (60%) NA NA
8 1478.467 1558.771 6.8688965 0.9009028 9 (18%) 14 (28%) 20 (40%) 7 (14%) NA
8 1479.776 1579.201 7.9328808 0.9014205 8 (16%) 11 (22%) 5 (10%) 20 (40%) 6 (12%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 5 19 26
participant_age (mean (SD)) 37.8 (11.7) 42.2 (14.4) 44.1 (12.7) 0.33
duration_symptoms_months (mean (SD)) 17.2 (12.6) 15.3 (9.7) 17.1 (9.5) 0.12
bmi (mean (SD)) 24.9 (4.4) 29.4 (7.7) 27.7 (5.9) 0.5
participant_sex = Male (%) 2 (40) 10 (52.6) 9 (34.6) 0.24
race (%) 0.58
Asian 0 (0) 1 (5.3) 3 (11.5)
Black or African American 0 (0) 1 (5.3) 1 (3.8)
White 5 (100) 15 (78.9) 20 (76.9)
More than one race 0 (0) 1 (5.3) 1 (3.8)
Other 0 (0) 1 (5.3) 1 (3.8)
ethnic = 1 (%) 0 (0) 2 (10.5) 4 (15.4) 0.41
bmi_group (%) 0.49
Underweight 0 (0) 1 (5.3) 1 (3.8)
Normal 3 (60) 6 (31.6) 9 (34.6)
Overweight 1 (20) 4 (21.1) 7 (26.9)
Obese 1 (20) 8 (42.1) 9 (34.6)
fatigue = 1 (%) 5 (100) 18 (94.7) 24 (92.3) 0.28
sob = 1 (%) 5 (100) 11 (57.9) 10 (38.5) 1.13
brainfog = 1 (%) 4 (80) 15 (78.9) 22 (84.6) 0.1
bodyaches = 1 (%) 4 (80) 9 (47.4) 15 (57.7) 0.48
heart = 1 (%) 5 (100) 8 (42.1) 15 (57.7) 1.06
stomach = 1 (%) 2 (40) 8 (42.1) 11 (42.3) 0.03
rand_assignment = Treatment (%) 4 (80) 14 (73.7) 19 (73.1) 0.11
high_phys (mean (SD)) 11.4 (3.1) 20.6 (3.6) 31.2 (4.5) 3.47
low_phys (mean (SD)) 35.3 (7.7) 27.8 (5.2) 19.1 (4.3) 1.85
rel_phys (mean (SD)) -0.5 (0.1) -0.1 (0.1) 0.2 (0.1) 4.57
mean_peak_phys (mean (SD)) 1424.4 (139.8) 1608.8 (60) 1687 (49.7) 1.88
heartRate_median_dt (mean (SD)) 68.5 (3.8) 71.8 (6.8) 76.4 (10.2) 0.72
heart_rate_pct5 (mean (SD)) 56.7 (3.4) 59 (7.1) 61.7 (8.3) 0.51
heart_rate_pct95 (mean (SD)) 91.6 (7.3) 97.1 (9.8) 102.2 (13) 0.69
heartRate_std_dt (mean (SD)) 11.3 (2) 12.4 (3.5) 13.1 (3.7) 0.39
heartRateVariability_median_dt (mean (SD)) 39.8 (11.8) 38.6 (19.3) 37.3 (17.5) 0.1
restingHeartRate_median_dt (mean (SD)) 57.2 (4.2) 60.1 (6.2) 62.9 (8.8) 0.59
walkingHeartRateAverage_median_dt (mean (SD)) 96.3 (17.5) 95.4 (10.2) 97.1 (12.8) 0.09
bloodOxygenSaturation_median_dt (mean (SD)) 97.3 (0.6) 96.3 (1.4) 96.2 (1) 0.84
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 94.1 (1.4) 93.1 (1.9) 93.7 (1.3) 0.44
stepCount_median_dt (mean (SD)) 148.3 (221) 766 (448.7) 2484.5 (1193) 2.12
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 5.319573e+04 5.321485e+04 0.0195742 0.9994352 1 (2%) 47 (94%) NA NA NA
2 2.000000e+09 2.000000e+09 0.0000000 1.0000000 0 (0%) 0 (0%) 0 (0%) NA NA
2 5.316525e+04 5.319966e+04 2.4569409 0.9645538 12 (24%) 1 (2%) 2 (4%) 33 (66%) NA
2 5.324985e+04 5.329192e+04 0.0220474 0.9997260 0 (0%) 0 (0%) 48 (96%) 0 (0%) 0 (0%)
4 5.319627e+04 5.322303e+04 0.0213208 0.9993848 1 (2%) 47 (94%) NA NA NA
4 5.324408e+04 5.328232e+04 0.0068420 0.9998754 0 (0%) 48 (96%) 0 (0%) NA NA
4 2.000000e+09 2.000000e+09 0.0000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) NA
4 5.323555e+04 5.329674e+04 0.1006799 0.9987489 1 (2%) 0 (0%) 47 (94%) 0 (0%) 0 (0%)
6 5.317670e+04 5.321111e+04 0.0021074 0.9999392 1 (2%) 47 (94%) NA NA NA
6 5.317219e+04 5.322190e+04 4.4330425 0.9192974 1 (2%) 16 (32%) 31 (62%) NA NA
6 2.000000e+09 2.000000e+09 0.0000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) NA
6 2.000000e+09 2.000000e+09 0.0000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%)
8 5.318223e+04 5.322429e+04 0.0568774 0.9983589 2 (4%) 46 (92%) NA NA NA
8 5.315714e+04 5.321833e+04 0.5590216 0.9898231 2 (4%) 3 (6%) 43 (86%) NA NA
8 5.322223e+04 5.330253e+04 0.0569536 0.9991783 2 (4%) 0 (0%) 46 (92%) 0 (0%) NA
8 2.000000e+09 2.000000e+09 0.0000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 SMD
n 1 47
participant_age (mean (SD)) 34 (NA) 43.1 (13.1)
duration_symptoms_months (mean (SD)) 4.6 (NA) 16.6 (9.6)
bmi (mean (SD)) 20.1 (NA) 28.3 (6.6)
participant_sex = Male (%) 1 (100) 20 (42.6) 1.64
race (%) 0.74
Asian 0 (0) 4 (8.5)
Black or African American 0 (0) 2 (4.3)
White 1 (100) 37 (78.7)
More than one race 0 (0) 2 (4.3)
Other 0 (0) 2 (4.3)
ethnic = 1 (%) 0 (0) 6 (12.8) 0.54
bmi_group (%) 1.97
Underweight 0 (0) 2 (4.3)
Normal 1 (100) 16 (34)
Overweight 0 (0) 11 (23.4)
Obese 0 (0) 18 (38.3)
fatigue = 1 (%) 1 (100) 44 (93.6) 0.37
sob = 1 (%) 1 (100) 23 (48.9) 1.45
brainfog = 1 (%) 1 (100) 39 (83) 0.64
bodyaches = 1 (%) 1 (100) 25 (53.2) 1.33
heart = 1 (%) 1 (100) 25 (53.2) 1.33
stomach = 1 (%) 1 (100) 19 (40.4) 1.72
rand_assignment = Treatment (%) 0 (0) 35 (74.5) 2.42
high_phys (mean (SD)) 9.9 (NA) 26.2 (7)
low_phys (mean (SD)) 25.2 (NA) 23.4 (7)
rel_phys (mean (SD)) -0.4 (NA) 0.1 (0.2)
mean_peak_phys (mean (SD)) 1243.7 (NA) 1649.4 (68.6)
heartRate_median_dt (mean (SD)) 64.8 (NA) 74.1 (9)
heart_rate_pct5 (mean (SD)) 55 (NA) 60.3 (7.8)
heart_rate_pct95 (mean (SD)) 85.7 (NA) 99.6 (11.9)
heartRate_std_dt (mean (SD)) 9.7 (NA) 12.7 (3.6)
heartRateVariability_median_dt (mean (SD)) 55.9 (NA) 37.9 (17.7)
restingHeartRate_median_dt (mean (SD)) 54.8 (NA) 61.4 (7.8)
walkingHeartRateAverage_median_dt (mean (SD)) 77.7 (NA) 96.1 (11.8)
bloodOxygenSaturation_median_dt (mean (SD)) 96.9 (NA) 96.3 (1.1)
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 93.3 (NA) 93.4 (1.6)
stepCount_median_dt (mean (SD)) 534.8 (NA) 1687.5 (1294)
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 6.197886e+04 6.199798e+04 4.077341 0.8823528 31 (62%) 13 (26%) NA NA NA
2 6.195170e+04 6.197847e+04 2.447676 0.9554406 25 (50%) 14 (28%) 5 (10%) NA NA
2 6.195441e+04 6.198883e+04 9.190968 0.8674024 21 (42%) 6 (12%) 12 (24%) 5 (10%) NA
2 6.193175e+04 6.197381e+04 5.976847 0.9257275 21 (42%) 7 (14%) 2 (4%) 9 (18%) 5 (10%)
4 6.198017e+04 6.200693e+04 3.554579 0.8974365 31 (62%) 13 (26%) NA NA NA
4 2.000000e+09 2.000000e+09 0.000000 1.0000000 0 (0%) 0 (0%) 0 (0%) NA NA
4 6.195714e+04 6.200685e+04 5.908291 0.9147614 22 (44%) 9 (18%) 8 (16%) 4 (8%) NA
4 2.000000e+09 2.000000e+09 0.000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%)
6 6.197568e+04 6.201009e+04 3.983770 0.8850527 31 (62%) 13 (26%) NA NA NA
6 6.196032e+04 6.201004e+04 1.641569 0.9701156 25 (50%) 14 (28%) 5 (10%) NA NA
6 6.195043e+04 6.201544e+04 4.667842 0.9326573 24 (48%) 4 (8%) 10 (20%) 5 (10%) NA
6 6.196643e+04 6.204673e+04 4.658686 0.9421079 0 (0%) 24 (48%) 4 (8%) 10 (20%) 5 (10%)
8 6.197265e+04 6.201472e+04 4.549177 0.8687385 31 (62%) 13 (26%) NA NA NA
8 6.195003e+04 6.201121e+04 1.604478 0.9707908 25 (50%) 14 (28%) 5 (10%) NA NA
8 2.000000e+09 2.000000e+09 0.000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) NA
8 2.000000e+09 2.000000e+09 0.000000 1.0000000 0 (0%) 0 (0%) 0 (0%) 0 (0%) 0 (0%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 25 14 5
participant_age (mean (SD)) 42.6 (10.2) 44.6 (15.4) 43.2 (14) 0.1
duration_symptoms_months (mean (SD)) 11.1 (6.5) 23.3 (7.7) 20.6 (11.6) 1
bmi (mean (SD)) 26.5 (5.3) 31.1 (7.1) 25.9 (6.3) 0.54
participant_sex = Male (%) 12 (48) 6 (42.9) 1 (20) 0.41
race (%) 0.75
Asian 3 (12) 1 (7.1) 0 (0)
Black or African American 1 (4) 0 (0) 1 (20)
White 19 (76) 11 (78.6) 4 (80)
More than one race 1 (4) 1 (7.1) 0 (0)
Other 1 (4) 1 (7.1) 0 (0)
ethnic = 1 (%) 2 (8) 4 (28.6) 0 (0) 0.62
bmi_group (%) 0.84
Underweight 1 (4) 0 (0) 1 (20)
Normal 11 (44) 3 (21.4) 1 (20)
Overweight 6 (24) 3 (21.4) 2 (40)
Obese 7 (28) 8 (57.1) 1 (20)
fatigue = 1 (%) 24 (96) 12 (85.7) 5 (100) 0.41
sob = 1 (%) 11 (44) 8 (57.1) 3 (60) 0.22
brainfog = 1 (%) 21 (84) 12 (85.7) 3 (60) 0.4
bodyaches = 1 (%) 15 (60) 8 (57.1) 4 (80) 0.34
heart = 1 (%) 14 (56) 8 (57.1) 4 (80) 0.35
stomach = 1 (%) 6 (24) 8 (57.1) 4 (80) 0.86
rand_assignment = Treatment (%) 17 (68) 10 (71.4) 4 (80) 0.18
high_phys (mean (SD)) 18.6 (5.4) 29.1 (8.2) 44.4 (14.7) 1.71
low_phys (mean (SD)) 81.4 (5.4) 70.9 (8.2) 55.6 (14.7) 1.71
rel_phys (mean (SD)) -0.6 (0.1) -0.4 (0.2) -0.1 (0.3) 1.71
mean_peak_phys (mean (SD)) 288.7 (98.7) 678 (105.5) 1150.9 (154.5) 4.68
heartRate_median_n (mean (SD)) 62 (8.9) 66.2 (11) 69.2 (6.3) 0.56
heart_rate_pct5 (mean (SD)) 57.3 (8.5) 60 (9) 62 (6.5) 0.39
heart_rate_pct95 (mean (SD)) 68.7 (9.2) 76.5 (13.8) 83.2 (4.2) 1.11
heartRate_std_n (mean (SD)) 3.9 (0.7) 5.6 (2) 7.2 (1.7) 1.56
heartRateVariability_median_n (mean (SD)) 43.5 (22.7) 43.4 (20.3) 38.6 (15.2) 0.17
restingHeartRate_median_n (mean (SD)) 62.2 (10.8) 64 (9.6) 63.7 (8.1) 0.12
walkingHeartRateAverage_median_n (mean (SD)) 86 (11.2) 94.2 (17.2) 95.8 (9.9) 0.53
bloodOxygenSaturation_median_n (mean (SD)) 96.1 (0.9) 95.7 (1) 95.3 (0.3) 0.71
bloodOxygenSaturation_percentile_5_n (mean (SD)) 93.8 (1.2) 93.3 (1.5) 93.1 (0.2) 0.44
stepCount_median_n (mean (SD)) 0 (0.2) 0.2 (0.5) 0.5 (0.5) 0.67
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 25490.06 25508.98 7.4973387 0.7792577 40 (81.63%) 9 (18.37%) NA NA NA
2 25488.88 25515.36 12.5228441 0.7673718 18 (36.73%) 25 (51.02%) 6 (12.24%) NA NA
2 25478.43 25512.49 5.9516995 0.9123828 22 (44.9%) 9 (18.37%) 13 (26.53%) 5 (10.2%) NA
2 25468.39 25510.01 6.8560333 0.9130634 13 (26.53%) 17 (34.69%) 7 (14.29%) 9 (18.37%) 3 (6.12%)
4 25488.90 25515.39 2.4692886 0.9272973 46 (93.88%) 3 (6.12%) NA NA NA
4 25500.90 25538.74 2.4694876 0.9541260 0 (0%) 46 (93.88%) 3 (6.12%) NA NA
4 25497.81 25547.00 8.5819025 0.8736626 41 (83.67%) 4 (8.16%) 2 (4.08%) 2 (4.08%) NA
4 25501.46 25562.00 12.3670995 0.8431814 1 (2.04%) 2 (4.08%) 28 (57.14%) 16 (32.65%) 2 (4.08%)
6 25478.78 25512.83 0.2682189 0.9921029 47 (95.92%) 2 (4.08%) NA NA NA
6 25487.54 25536.73 6.0278113 0.8880255 42 (85.71%) 4 (8.16%) 3 (6.12%) NA NA
6 25476.28 25540.60 15.9290140 0.7655030 29 (59.18%) 1 (2.04%) 17 (34.69%) 2 (4.08%) NA
6 25493.08 25572.54 13.9475877 0.8231403 1 (2.04%) 19 (38.78%) 1 (2.04%) 25 (51.02%) 3 (6.12%)
8 25483.10 25524.72 13.5975638 0.5996502 29 (59.18%) 20 (40.82%) NA NA NA
8 25466.54 25527.08 11.2052084 0.7918486 7 (14.29%) 22 (44.9%) 20 (40.82%) NA NA
8 25460.81 25540.26 11.1080618 0.8364740 5 (10.2%) 21 (42.86%) 19 (38.78%) 4 (8.16%) NA
8 25464.87 25563.24 10.1294493 0.8715555 2 (4.08%) 7 (14.29%) 19 (38.78%) 18 (36.73%) 3 (6.12%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 SMD
n 40 9
participant_age (mean (SD)) 44 (13.7) 37 (9.8) 0.58
duration_symptoms_months (mean (SD)) 16.1 (9.9) 18.3 (9.6) 0.22
bmi (mean (SD)) 28.2 (6.6) 28 (6.9) 0.03
participant_sex = Male (%) 19 (47.5) 2 (22.2) 0.55
race (%) 0.63
Asian 3 (7.5) 1 (11.1)
Black or African American 1 (2.5) 1 (11.1)
White 33 (82.5) 6 (66.7)
More than one race 2 (5) 0 (0)
Other 1 (2.5) 1 (11.1)
ethnic = 1 (%) 3 (7.5) 3 (33.3) 0.68
bmi_group (%) 0.5
Underweight 1 (2.5) 1 (11.1)
Normal 15 (37.5) 2 (22.2)
Overweight 9 (22.5) 3 (33.3)
Obese 15 (37.5) 3 (33.3)
fatigue = 1 (%) 39 (97.5) 7 (77.8) 0.63
sob = 1 (%) 23 (57.5) 3 (33.3) 0.5
brainfog = 1 (%) 33 (82.5) 7 (77.8) 0.12
bodyaches = 1 (%) 23 (57.5) 4 (44.4) 0.26
heart = 1 (%) 23 (57.5) 5 (55.6) 0.04
stomach = 1 (%) 18 (45) 3 (33.3) 0.24
rand_assignment = Treatment (%) 31 (77.5) 6 (66.7) 0.24
high_phys (mean (SD)) 24.1 (7.6) 29.1 (8.7) 0.62
low_phys (mean (SD)) 25.3 (7.3) 18.5 (5.8) 1.03
rel_phys (mean (SD)) 0 (0.3) 0.2 (0.3) 0.87
mean_peak_phys (mean (SD)) 1622.4 (104.9) 1660 (88.3) 0.39
heartRate_median_dt (mean (SD)) 70.8 (6.5) 86.8 (5.5) 2.66
heart_rate_pct5 (mean (SD)) 58.1 (6.5) 69.3 (4.9) 1.95
heart_rate_pct95 (mean (SD)) 95.8 (8.8) 113.9 (12.2) 1.7
heartRate_std_dt (mean (SD)) 12.2 (3.2) 14.4 (4.5) 0.56
heartRateVariability_median_dt (mean (SD)) 38.4 (17.8) 36.5 (16.7) 0.11
restingHeartRate_median_dt (mean (SD)) 59.1 (6.4) 70.5 (5.5) 1.9
walkingHeartRateAverage_median_dt (mean (SD)) 93.5 (11) 109 (8.4) 1.59
bloodOxygenSaturation_median_dt (mean (SD)) 96.3 (1.2) 96.3 (1) 0
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 93.4 (1.6) 93.8 (1.6) 0.27
stepCount_median_dt (mean (SD)) 1484.9 (1314.1) 1915.2 (1223.5) 0.34
beta_blockers = Yes (%) 8 (20) 2 (22.2) 0.05
calcium_channel_blockers = Yes (%) 2 (5) 0 (0) 0.32
adderall = Yes (%) 1 (2.5) 0 (0) 0.23
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 25478.78 25512.83 0.2682189 0.9921029 47 (95.92%) 2 (4.08%) NA NA NA
2 25487.54 25536.73 6.0278113 0.8880255 42 (85.71%) 4 (8.16%) 3 (6.12%) NA NA
2 25476.28 25540.60 15.9290140 0.7655030 29 (59.18%) 1 (2.04%) 17 (34.69%) 2 (4.08%) NA
2 25493.08 25572.54 13.9475877 0.8231403 1 (2.04%) 19 (38.78%) 1 (2.04%) 25 (51.02%) 3 (6.12%)
4 25483.10 25524.72 13.5975638 0.5996502 29 (59.18%) 20 (40.82%) NA NA NA
4 25466.54 25527.08 11.2052084 0.7918486 7 (14.29%) 22 (44.9%) 20 (40.82%) NA NA
4 25460.81 25540.26 11.1080618 0.8364740 5 (10.2%) 21 (42.86%) 19 (38.78%) 4 (8.16%) NA
4 25464.87 25563.24 10.1294493 0.8715555 2 (4.08%) 7 (14.29%) 19 (38.78%) 18 (36.73%) 3 (6.12%)
6 24953.47 24972.38 9.9704582 0.7064422 30 (61.22%) 19 (38.78%) NA NA NA
6 24940.98 24967.47 6.1080444 0.8865351 26 (53.06%) 22 (44.9%) 1 (2.04%) NA NA
6 24932.53 24966.58 7.4645671 0.8901113 6 (12.24%) 20 (40.82%) 18 (36.73%) 5 (10.2%) NA
6 24914.91 24956.53 7.5165736 0.9046876 6 (12.24%) 20 (40.82%) 14 (28.57%) 8 (16.33%) 1 (2.04%)
8 24958.49 24984.97 10.1531882 0.7010622 30 (61.22%) 19 (38.78%) NA NA NA
8 24944.45 24982.29 5.8572587 0.8911937 26 (53.06%) 22 (44.9%) 1 (2.04%) NA NA
8 24940.65 24989.84 4.8931543 0.9279660 2 (4.08%) 24 (48.98%) 20 (40.82%) 3 (6.12%) NA
8 24924.60 24985.14 6.5952583 0.9163701 6 (12.24%) 20 (40.82%) 13 (26.53%) 9 (18.37%) 1 (2.04%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 Class 4 SMD
n 6 20 18 5
participant_age (mean (SD)) 51.7 (16.9) 43.3 (13.7) 40.2 (11.1) 38.4 (13.3) 0.5
duration_symptoms_months (mean (SD)) 20.2 (13.8) 14.3 (9) 17.8 (9.2) 16.6 (10.8) 0.29
bmi (mean (SD)) 27.7 (5.8) 27.3 (5.1) 29.6 (7.8) 27.1 (9.3) 0.18
participant_sex = Male (%) 6 (100) 11 (55) 3 (16.7) 1 (20) 1.5
race (%) 0.8
Asian 2 (33.3) 0 (0) 1 (5.6) 1 (20)
Black or African American 0 (0) 0 (0) 2 (11.1) 0 (0)
White 4 (66.7) 18 (90) 13 (72.2) 4 (80)
More than one race 0 (0) 1 (5) 1 (5.6) 0 (0)
Other 0 (0) 1 (5) 1 (5.6) 0 (0)
ethnic = 1 (%) 0 (0) 2 (10) 3 (16.7) 1 (20) 0.4
bmi_group (%) 0.61
Underweight 0 (0) 0 (0) 1 (5.6) 1 (20)
Normal 2 (33.3) 9 (45) 4 (22.2) 2 (40)
Overweight 2 (33.3) 4 (20) 5 (27.8) 1 (20)
Obese 2 (33.3) 7 (35) 8 (44.4) 1 (20)
fatigue = 1 (%) 5 (83.3) 20 (100) 17 (94.4) 4 (80) 0.43
sob = 1 (%) 2 (33.3) 12 (60) 10 (55.6) 2 (40) 0.33
brainfog = 1 (%) 5 (83.3) 18 (90) 13 (72.2) 4 (80) 0.25
bodyaches = 1 (%) 2 (33.3) 13 (65) 9 (50) 3 (60) 0.36
heart = 1 (%) 2 (33.3) 12 (60) 9 (50) 5 (100) 0.94
stomach = 1 (%) 2 (33.3) 8 (40) 8 (44.4) 3 (60) 0.29
rand_assignment = Treatment (%) 5 (83.3) 14 (70) 14 (77.8) 4 (80) 0.17
high_phys (mean (SD)) 28.9 (8.6) 19.2 (6.5) 30.9 (13.3) 24.3 (10.8) 0.69
low_phys (mean (SD)) 71.2 (8.6) 80.8 (6.5) 69.1 (13.3) 75.7 (10.8) 0.69
rel_phys (mean (SD)) -0.4 (0.2) -0.6 (0.1) -0.4 (0.3) -0.5 (0.2) 0.69
mean_peak_phys (mean (SD)) 462 (192.2) 420.2 (275.5) 672 (357.4) 625.8 (302.4) 0.53
heartRate_median_n (mean (SD)) 50 (4.2) 59.7 (2.7) 69.6 (3.5) 81.8 (5) 4.36
heart_rate_pct5 (mean (SD)) 46.3 (4.1) 54.7 (2.5) 63.3 (3.8) 72.7 (5.7) 3.46
heart_rate_pct95 (mean (SD)) 55.8 (5.1) 67.8 (4.9) 79.9 (4.3) 92.8 (7.7) 3.64
heartRate_std_n (mean (SD)) 3.4 (0.6) 4.5 (1.6) 5.7 (1.8) 6.7 (2.2) 1.18
heartRateVariability_median_n (mean (SD)) 58.9 (37) 45 (17.8) 38.3 (10.8) 32 (16.2) 0.64
restingHeartRate_median_n (mean (SD)) 46.7 (5.9) 60.5 (5.7) 65.6 (4.6) 75.7 (5.1) 2.84
walkingHeartRateAverage_median_n (mean (SD)) 71.9 (9.4) 86.3 (10.8) 98.3 (9.2) 106.7 (13.3) 1.82
bloodOxygenSaturation_median_n (mean (SD)) 95.8 (0.5) 96.1 (1) 95.9 (1.2) 95.9 (0.7) 0.17
bloodOxygenSaturation_percentile_5_n (mean (SD)) 93.8 (0.8) 93.8 (1.2) 93.4 (1.6) 93.6 (0.6) 0.21
stepCount_median_n (mean (SD)) 0 (0) 0.1 (0.2) 0.2 (0.3) 0.5 (0.8) 0.63
beta_blockers = Yes (%) 1 (16.7) 4 (20) 3 (16.7) 2 (40) 0.28
calcium_channel_blockers = Yes (%) 0 (0) 1 (5) 1 (5.6) 0 (0) 0.23
adderall = Yes (%) 0 (0) 0 (0) 1 (5.6) 0 (0) 0.17
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 22384.70 22403.62 9.2445033 0.7278163 34 (69.39%) 15 (30.61%) NA NA NA
2 22372.16 22398.64 7.7045641 0.8568776 18 (36.73%) 21 (42.86%) 10 (20.41%) NA NA
2 22343.29 22377.35 4.2039498 0.9381121 5 (10.2%) 18 (36.73%) 16 (32.65%) 10 (20.41%) NA
2 22346.54 22388.16 8.3964309 0.8935307 5 (10.2%) 15 (30.61%) 13 (26.53%) 6 (12.24%) 10 (20.41%)
4 22389.79 22416.28 9.2350087 0.7280959 34 (69.39%) 15 (30.61%) NA NA NA
4 22381.46 22419.30 7.6694832 0.8575293 18 (36.73%) 21 (42.86%) 10 (20.41%) NA NA
4 22356.33 22405.52 4.1273974 0.9392390 18 (36.73%) 16 (32.65%) 5 (10.2%) 10 (20.41%) NA
4 22362.80 22423.34 8.1983684 0.8960422 5 (10.2%) 15 (30.61%) 12 (24.49%) 7 (14.29%) 10 (20.41%)
6 22391.00 22425.05 1.4456930 0.9574348 47 (95.92%) 2 (4.08%) NA NA NA
6 22380.60 22429.78 7.5780572 0.8592277 16 (32.65%) 23 (46.94%) 10 (20.41%) NA NA
6 22361.79 22426.11 4.0957146 0.9397054 5 (10.2%) 19 (38.78%) 15 (30.61%) 10 (20.41%) NA
6 22362.93 22442.38 6.5523836 0.9169138 2 (4.08%) 16 (32.65%) 14 (28.57%) 7 (14.29%) 10 (20.41%)
8 22347.34 22388.96 0.6472501 0.9809432 43 (87.76%) 6 (12.24%) NA NA NA
8 22347.32 22407.86 8.5363907 0.8414254 32 (65.31%) 11 (22.45%) 6 (12.24%) NA NA
8 22354.15 22433.61 13.8482837 0.7961342 24 (48.98%) 11 (22.45%) 8 (16.33%) 6 (12.24%) NA
8 22370.41 22468.79 13.0557018 0.8344497 12 (24.49%) 6 (12.24%) 7 (14.29%) 13 (26.53%) 11 (22.45%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 Class 4 SMD
n 5 18 16 10
participant_age (mean (SD)) 57.2 (18.9) 42.2 (11) 38.5 (12.5) 43 (12) 0.63
duration_symptoms_months (mean (SD)) 18.4 (14.4) 16.8 (9.8) 18.1 (10.6) 12.6 (5.3) 0.34
bmi (mean (SD)) 29 (5.6) 27.3 (5.2) 28.7 (7.4) 28.5 (8.5) 0.14
participant_sex = Male (%) 5 (100) 10 (55.6) 5 (31.2) 1 (10) 1.63
race (%) 0.86
Asian 1 (20) 1 (5.6) 0 (0) 2 (20)
Black or African American 0 (0) 1 (5.6) 0 (0) 1 (10)
White 4 (80) 15 (83.3) 15 (93.8) 5 (50)
More than one race 0 (0) 1 (5.6) 0 (0) 1 (10)
Other 0 (0) 0 (0) 1 (6.2) 1 (10)
ethnic = 1 (%) 0 (0) 1 (5.6) 2 (12.5) 3 (30) 0.53
bmi_group (%) 0.62
Underweight 0 (0) 0 (0) 1 (6.2) 1 (10)
Normal 1 (20) 9 (50) 4 (25) 3 (30)
Overweight 2 (40) 2 (11.1) 6 (37.5) 2 (20)
Obese 2 (40) 7 (38.9) 5 (31.2) 4 (40)
fatigue = 1 (%) 4 (80) 18 (100) 16 (100) 8 (80) 0.47
sob = 1 (%) 3 (60) 9 (50) 9 (56.2) 5 (50) 0.12
brainfog = 1 (%) 4 (80) 17 (94.4) 11 (68.8) 8 (80) 0.35
bodyaches = 1 (%) 1 (20) 10 (55.6) 11 (68.8) 5 (50) 0.56
heart = 1 (%) 2 (40) 9 (50) 11 (68.8) 6 (60) 0.33
stomach = 1 (%) 3 (60) 8 (44.4) 5 (31.2) 5 (50) 0.32
rand_assignment = Treatment (%) 4 (80) 13 (72.2) 13 (81.2) 7 (70) 0.16
high_phys (mean (SD)) 23.2 (3.3) 25.7 (7.5) 23.8 (9.5) 26.6 (8.1) 0.28
low_phys (mean (SD)) 24.4 (6.4) 25.6 (6.8) 24.1 (9.3) 21 (5.9) 0.34
rel_phys (mean (SD)) 0 (0.2) 0 (0.2) 0 (0.3) 0.1 (0.3) 0.27
mean_peak_phys (mean (SD)) 1650.1 (51.8) 1631.6 (115.5) 1620.8 (115.9) 1628.4 (81.2) 0.18
heartRate_median_dt (mean (SD)) 61 (3.3) 68.3 (3.4) 76.8 (5) 85.2 (6.2) 2.94
heart_rate_pct5 (mean (SD)) 47.7 (3.9) 55.7 (1.9) 61.8 (1.9) 71.7 (2.5) 4.89
heart_rate_pct95 (mean (SD)) 90.1 (14.4) 95.2 (8.9) 101.6 (11.8) 106.7 (10.3) 0.81
heartRate_std_dt (mean (SD)) 13.7 (5.7) 12.9 (2.8) 12.8 (3.8) 11.3 (2.9) 0.32
heartRateVariability_median_dt (mean (SD)) 48 (37.1) 41.6 (14.9) 37.6 (14.3) 27.3 (6.8) 0.63
restingHeartRate_median_dt (mean (SD)) 49.4 (4.9) 56.7 (3.4) 63.6 (2.8) 71.5 (4.4) 3.04
walkingHeartRateAverage_median_dt (mean (SD)) 84.7 (14.9) 91.6 (10.8) 100.9 (9.8) 103.5 (9.5) 0.94
bloodOxygenSaturation_median_dt (mean (SD)) 95.6 (1.5) 96.3 (1) 96.9 (1.2) 95.8 (0.8) 0.63
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 92.8 (2) 93.5 (1.4) 94 (1.7) 93.1 (1.4) 0.42
stepCount_median_dt (mean (SD)) 709.8 (277.4) 1748.6 (1249.6) 1416.4 (1461.9) 1894.7 (1336.4) 0.62
beta_blockers = Yes (%) 1 (20) 4 (22.2) 2 (12.5) 3 (30) 0.23
calcium_channel_blockers = Yes (%) 1 (20) 1 (5.6) 0 (0) 0 (0) 0.42
adderall = Yes (%) 0 (0) 1 (5.6) 0 (0) 0 (0) 0.17
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 22983.00 23001.92 10.4711526 0.6917004 30 (61.22%) 19 (38.78%) NA NA NA
2 22977.62 23004.10 9.2614371 0.8279567 13 (26.53%) 24 (48.98%) 12 (24.49%) NA NA
2 22967.94 23001.99 8.0261910 0.8818434 2 (4.08%) 17 (34.69%) 20 (40.82%) 10 (20.41%) NA
2 22941.49 22983.11 5.0328034 0.9361825 2 (4.08%) 20 (40.82%) 15 (30.61%) 10 (20.41%) 2 (4.08%)
4 22986.05 23012.53 9.5973062 0.7174289 30 (61.22%) 19 (38.78%) NA NA NA
4 22985.44 23023.27 9.4428693 0.8245863 13 (26.53%) 24 (48.98%) 12 (24.49%) NA NA
4 22976.95 23026.14 5.6577647 0.9167099 2 (4.08%) 26 (53.06%) 17 (34.69%) 4 (8.16%) NA
4 22954.46 23015.00 4.9528594 0.9371962 2 (4.08%) 15 (30.61%) 20 (40.82%) 10 (20.41%) 2 (4.08%)
6 22975.50 23009.55 2.2930009 0.9324877 45 (91.84%) 4 (8.16%) NA NA NA
6 22974.55 23023.74 9.1330827 0.8303410 23 (46.94%) 21 (42.86%) 5 (10.2%) NA NA
6 22975.66 23039.98 6.0561731 0.9108448 2 (4.08%) 21 (42.86%) 17 (34.69%) 9 (18.37%) NA
6 22957.69 23037.15 5.8436007 0.9259014 2 (4.08%) 19 (38.78%) 16 (32.65%) 8 (16.33%) 4 (8.16%)
8 22933.08 22974.70 0.9838782 0.9710319 43 (87.76%) 6 (12.24%) NA NA NA
8 22932.23 22992.76 8.8526437 0.8355505 10 (20.41%) 32 (65.31%) 7 (14.29%) NA NA
8 22933.86 23013.32 9.2389756 0.8639895 25 (51.02%) 12 (24.49%) 7 (14.29%) 5 (10.2%) NA
8 22944.42 23042.79 10.7078735 0.8642209 22 (44.9%) 7 (14.29%) 10 (20.41%) 3 (6.12%) 7 (14.29%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 SMD
n 43 6
participant_age (mean (SD)) 43.2 (13.6) 39.2 (11.5) 0.32
duration_symptoms_months (mean (SD)) 16.6 (9.7) 16.1 (11) 0.05
bmi (mean (SD)) 28.3 (6.3) 27.1 (8.9) 0.15
participant_sex = Male (%) 20 (46.5) 1 (16.7) 0.68
race (%) 0.77
Asian 3 (7) 1 (16.7)
Black or African American 2 (4.7) 0 (0)
White 35 (81.4) 4 (66.7)
More than one race 2 (4.7) 0 (0)
Other 1 (2.3) 1 (16.7)
ethnic = 1 (%) 4 (9.3) 2 (33.3) 0.61
bmi_group (%) 1.04
Underweight 1 (2.3) 1 (16.7)
Normal 14 (32.6) 3 (50)
Overweight 12 (27.9) 0 (0)
Obese 16 (37.2) 2 (33.3)
fatigue = 1 (%) 42 (97.7) 4 (66.7) 0.89
sob = 1 (%) 25 (58.1) 1 (16.7) 0.95
brainfog = 1 (%) 35 (81.4) 5 (83.3) 0.05
bodyaches = 1 (%) 25 (58.1) 2 (33.3) 0.51
heart = 1 (%) 23 (53.5) 5 (83.3) 0.68
stomach = 1 (%) 18 (41.9) 3 (50) 0.16
rand_assignment = Treatment (%) 32 (74.4) 5 (83.3) 0.22
high_phys (mean (SD)) 25.4 (11.4) 23.4 (10.2) 0.19
low_phys (mean (SD)) 74.6 (11.4) 76.7 (10.2) 0.19
rel_phys (mean (SD)) -0.5 (0.2) -0.5 (0.2) 0.19
mean_peak_phys (mean (SD)) 544.6 (324.5) 497.2 (283.4) 0.16
heartRate_median_n (mean (SD)) 62.4 (7.8) 78.6 (7.7) 2.08
heart_rate_pct5 (mean (SD)) 57 (7) 70.1 (6.5) 1.92
heart_rate_pct95 (mean (SD)) 71.1 (9.6) 89.4 (11.1) 1.77
heartRate_std_n (mean (SD)) 4.8 (1.7) 6.4 (2.5) 0.71
heartRateVariability_median_n (mean (SD)) 43.9 (20.3) 36.1 (13.2) 0.46
restingHeartRate_median_n (mean (SD)) 60.9 (8.6) 73.5 (6.5) 1.65
walkingHeartRateAverage_median_n (mean (SD)) 89 (13.4) 107.9 (12.3) 1.47
bloodOxygenSaturation_median_n (mean (SD)) 96 (0.9) 95.5 (1.2) 0.48
bloodOxygenSaturation_percentile_5_n (mean (SD)) 93.7 (1.2) 93 (1.3) 0.54
stepCount_median_n (mean (SD)) 0.1 (0.3) 0.4 (0.7) 0.6
beta_blockers = Yes (%) 9 (20.9) 1 (16.7) 0.11
calcium_channel_blockers = Yes (%) 2 (4.7) 0 (0) 0.31
adderall = Yes (%) 1 (2.3) 0 (0) 0.22
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 31809.60 31828.52 2.5554685 0.9247600 46 (93.88%) 3 (6.12%) NA NA NA
2 31813.21 31839.70 12.1013393 0.7752018 12 (24.49%) 35 (71.43%) 2 (4.08%) NA NA
2 31805.85 31839.90 5.6824494 0.9163465 7 (14.29%) 12 (24.49%) 28 (57.14%) 2 (4.08%) NA
2 31800.93 31842.55 7.2973067 0.9074679 7 (14.29%) 5 (10.2%) 19 (38.78%) 16 (32.65%) 2 (4.08%)
4 31793.65 31820.14 0.3127915 0.9907906 46 (93.88%) 3 (6.12%) NA NA NA
4 31776.86 31814.70 0.2849164 0.9947073 45 (91.84%) 1 (2.04%) 3 (6.12%) NA NA
4 31801.55 31850.73 9.2483993 0.8638508 6 (12.24%) 34 (69.39%) 6 (12.24%) 3 (6.12%) NA
4 31807.98 31868.52 14.3990970 0.8174151 25 (51.02%) 6 (12.24%) 10 (20.41%) 5 (10.2%) 3 (6.12%)
6 31785.21 31819.26 0.3243472 0.9904503 46 (93.88%) 3 (6.12%) NA NA NA
6 31794.51 31843.70 2.0007917 0.9628327 2 (4.08%) 44 (89.8%) 3 (6.12%) NA NA
6 31773.90 31838.22 0.7244019 0.9893358 1 (2.04%) 44 (89.8%) 1 (2.04%) 3 (6.12%) NA
6 31785.85 31865.30 8.9019555 0.8871205 1 (2.04%) 6 (12.24%) 37 (75.51%) 3 (6.12%) 2 (4.08%)
8 31794.70 31836.32 3.1820129 0.9063128 42 (85.71%) 7 (14.29%) NA NA NA
8 31769.52 31830.06 1.9755350 0.9633018 42 (85.71%) 5 (10.2%) 2 (4.08%) NA NA
8 31825.24 31904.69 4.4684866 0.9342177 2 (4.08%) 39 (79.59%) 0 (0%) 8 (16.33%) NA
8 31737.33 31835.70 6.4331538 0.9184256 36 (73.47%) 4 (8.16%) 1 (2.04%) 5 (10.2%) 3 (6.12%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 SMD
n 46 3
participant_age (mean (SD)) 43.5 (13.3) 30.7 (4) 1.3
duration_symptoms_months (mean (SD)) 16 (9.6) 24.5 (10.2) 0.86
bmi (mean (SD)) 27.9 (6.4) 31.7 (9.7) 0.46
participant_sex = Male (%) 20 (43.5) 1 (33.3) 0.21
race (%) 0.74
Asian 4 (8.7) 0 (0)
Black or African American 2 (4.3) 0 (0)
White 36 (78.3) 3 (100)
More than one race 2 (4.3) 0 (0)
Other 2 (4.3) 0 (0)
ethnic = 1 (%) 5 (10.9) 1 (33.3) 0.56
bmi_group (%) 0.36
Underweight 2 (4.3) 0 (0)
Normal 16 (34.8) 1 (33.3)
Overweight 11 (23.9) 1 (33.3)
Obese 17 (37) 1 (33.3)
fatigue = 1 (%) 43 (93.5) 3 (100) 0.37
sob = 1 (%) 24 (52.2) 2 (66.7) 0.3
brainfog = 1 (%) 38 (82.6) 2 (66.7) 0.37
bodyaches = 1 (%) 26 (56.5) 1 (33.3) 0.48
heart = 1 (%) 25 (54.3) 3 (100) 1.3
stomach = 1 (%) 20 (43.5) 1 (33.3) 0.21
rand_assignment = Treatment (%) 36 (78.3) 1 (33.3) 1.01
high_phys (mean (SD)) 24.7 (8) 29.8 (5.2) 0.74
low_phys (mean (SD)) 24.4 (7.6) 18 (1.2) 1.19
rel_phys (mean (SD)) 0 (0.3) 0.2 (0.1) 1.14
mean_peak_phys (mean (SD)) 1624.7 (101.9) 1700.2 (96.4) 0.76
heartRate_median_dt (mean (SD)) 72.7 (8) 89.7 (5.6) 2.45
heart_rate_pct5 (mean (SD)) 59.7 (7.4) 67 (7.8) 0.96
heart_rate_pct95 (mean (SD)) 97.2 (9.1) 128.1 (10.2) 3.2
heartRate_std_dt (mean (SD)) 12.1 (3) 19.6 (3.7) 2.22
heartRateVariability_median_dt (mean (SD)) 37.1 (17.1) 53.1 (20.1) 0.86
restingHeartRate_median_dt (mean (SD)) 60.6 (7.2) 70.4 (9.3) 1.17
walkingHeartRateAverage_median_dt (mean (SD)) 94.9 (11) 118.3 (6.3) 2.62
bloodOxygenSaturation_median_dt (mean (SD)) 96.3 (1.2) 96.6 (0.5) 0.28
bloodOxygenSaturation_percentile_5_dt (mean (SD)) 93.5 (1.6) 93.9 (1.2) 0.32
stepCount_median_dt (mean (SD)) 1537.7 (1315.2) 1966.4 (1079.7) 0.36
beta_blockers = Yes (%) 10 (21.7) 0 (0) 0.74
calcium_channel_blockers = Yes (%) 2 (4.3) 0 (0) 0.3
adderall = Yes (%) 1 (2.2) 0 (0) 0.21
Number of knots AIC BIC Entropy Relative entropy Class 1 Class 2 Class 3 Class 4 Class 5
2 29573.83 29592.74 8.7422570 0.7426039 26 (53.06%) 23 (46.94%) NA NA NA
2 29546.43 29572.92 5.2933513 0.9016691 24 (48.98%) 23 (46.94%) 2 (4.08%) NA NA
2 29540.01 29574.06 4.6607232 0.9313877 2 (4.08%) 24 (48.98%) 21 (42.86%) 2 (4.08%) NA
2 29537.77 29579.39 9.7198601 0.8767492 2 (4.08%) 17 (34.69%) 9 (18.37%) 19 (38.78%) 2 (4.08%)
4 29557.41 29583.89 0.9544556 0.9718982 46 (93.88%) 3 (6.12%) NA NA NA
4 29544.94 29582.78 4.9862408 0.9073740 25 (51.02%) 22 (44.9%) 2 (4.08%) NA NA
4 29540.03 29589.22 3.9562654 0.9417583 2 (4.08%) 24 (48.98%) 21 (42.86%) 2 (4.08%) NA
4 29542.29 29602.82 8.9400711 0.8866372 2 (4.08%) 17 (34.69%) 7 (14.29%) 21 (42.86%) 2 (4.08%)
6 29557.13 29591.19 0.6902523 0.9796771 46 (93.88%) 3 (6.12%) NA NA NA
6 29549.26 29598.44 5.4009762 0.8996698 24 (48.98%) 22 (44.9%) 3 (6.12%) NA NA
6 29551.20 29615.52 4.4996126 0.9337595 2 (4.08%) 24 (48.98%) 20 (40.82%) 3 (6.12%) NA
6 29545.02 29624.48 8.8866805 0.8873142 2 (4.08%) 24 (48.98%) 14 (28.57%) 6 (12.24%) 3 (6.12%)
8 29545.65 29587.27 0.0522288 0.9984622 46 (93.88%) 3 (6.12%) NA NA NA
8 29500.26 29560.79 0.5551663 0.9896871 44 (89.8%) 2 (4.08%) 3 (6.12%) NA NA
8 29559.02 29638.48 4.6395553 0.9316994 2 (4.08%) 24 (48.98%) 20 (40.82%) 3 (6.12%) NA
8 29528.91 29627.28 7.1662640 0.9091296 2 (4.08%) 24 (48.98%) 16 (32.65%) 5 (10.2%) 2 (4.08%)

Mean predicted and empirical trajectories of classes for models with lowest BIC:

The simplest model (considering the number of classes and knots) was chosen as the final model from the three models with the lowest BIC.

Heatmap of the best model fit:

Baseline characteristics by class of best model fit:

Class 1 Class 2 Class 3 SMD
n 24 23 2
participant_age (mean (SD)) 47 (13.9) 39.3 (11.5) 29 (2.8) 1.21
duration_symptoms_months (mean (SD)) 13.9 (9.6) 19.5 (9.8) 14.5 (1) 0.46
bmi (mean (SD)) 27.5 (5.3) 29.2 (7.9) 24.5 (0.5) 0.63
participant_sex = Male (%) 15 (62.5) 5 (21.7) 1 (50) 0.59
race (%) 0.64
Asian 2 (8.3) 2 (8.7) 0 (0)
Black or African American 0 (0) 2 (8.7) 0 (0)
White 20 (83.3) 17 (73.9) 2 (100)
More than one race 1 (4.2) 1 (4.3) 0 (0)
Other 1 (4.2) 1 (4.3) 0 (0)
ethnic = 1 (%) 2 (8.3) 3 (13) 1 (50) 0.68
bmi_group (%) 1.65
Underweight 0 (0) 2 (8.7) 0 (0)
Normal 10 (41.7) 5 (21.7) 2 (100)
Overweight 5 (20.8) 7 (30.4) 0 (0)
Obese 9 (37.5) 9 (39.1) 0 (0)
fatigue = 1 (%) 23 (95.8) 22 (95.7) 1 (50) 0.8
sob = 1 (%) 12 (50) 14 (60.9) 0 (0) 1.13
brainfog = 1 (%) 21 (87.5) 18 (78.3) 1 (50) 0.58
bodyaches = 1 (%) 13 (54.2) 13 (56.5) 1 (50) 0.09
heart = 1 (%) 13 (54.2) 13 (56.5) 2 (100) 0.86
stomach = 1 (%) 9 (37.5) 10 (43.5) 2 (100) 1.19
rand_assignment = Treatment (%) 18 (75) 18 (78.3) 1 (50) 0.41
high_phys (mean (SD)) 20.2 (7.5) 29.6 (12.7) 34.3 (6.6) 1.12
low_phys (mean (SD)) 79.8 (7.5) 70.4 (12.7) 65.7 (6.6) 1.12
rel_phys (mean (SD)) -0.6 (0.1) -0.4 (0.2) -0.3 (0.1) 1.12
mean_peak_phys (mean (SD)) 371.9 (201.4) 697.3 (343.2) 720.4 (2) 1.23
heartRate_median_n (mean (SD)) 57.4 (5.5) 69.9 (5.7) 85.2 (7.2) 2.98
heart_rate_pct5 (mean (SD)) 52.9 (5.2) 63.2 (5.9) 75.1 (6.2) 2.58
heart_rate_pct95 (mean (SD)) 63.9 (6.1) 81 (4.8) 98.9 (10.3) 3.14
heartRate_std_n (mean (SD)) 3.8 (0.7) 6.1 (1.8) 7.9 (1.2) 2.33
heartRateVariability_median_n (mean (SD)) 44.7 (20.8) 41.9 (19.2) 33.1 (9.6) 0.48
restingHeartRate_median_n (mean (SD)) 54.9 (8.6) 66.6 (5.7) 77.6 (8.6) 1.91
walkingHeartRateAverage_median_n (mean (SD)) 79.2 (9.9) 98.7 (8.9) 116.9 (12.6) 2.35
bloodOxygenSaturation_median_n (mean (SD)) 96 (0.9) 95.9 (1.1) 96.1 (0.3) 0.18
bloodOxygenSaturation_percentile_5_n (mean (SD)) 93.8 (1.1) 93.5 (1.4) 94.2 (0.3) 0.45
stepCount_median_n (mean (SD)) 0 (0) 0.2 (0.4) 1.3 (0.5) 2.17
beta_blockers = Yes (%) 5 (20.8) 4 (17.4) 1 (50) 0.49
calcium_channel_blockers = Yes (%) 1 (4.2) 1 (4.3) 0 (0) 0.2
adderall = Yes (%) 0 (0) 1 (4.3) 0 (0) 0.2